There are numerous issues with your example: the relationship between dog and human is explicitly that of the family: the only social mechanism wolfs understand (a pack is little more than an extended family which bands together to hunt large prey, the social bonding lasts only for as long as the source of prey does). It might in fact come to regard other pets in your household as part of the same family. Within this family (or pack) there is a certain competition for the spot of top dog, and ill-disciplined dogs do display signs of competition towards their incompetent owners.
The fact that dogs bark towards humans (rather than growl) at first suggest that dogs treat us as dogs, not as humans and they'll proceed to sniff where they figure your genitals are. By contrast cats definitely understand the divide between humans and cats because they employ a different type of communication (the meow) towards us than they do towards other cats, and they will not approach until they have verified you are not a threat to them.
The real problem is however that dogs do not have any memory or intelligence anywhere near powerful enough to engage in such reflection. Dogs are every bit as devoid of intellectual thought as ants are[*], and considerably less clever than cats or pidgeons (both species have to perform far more complex mental exercises to survive). [*] Perhaps even more so as a colony of ants is capable of far more complex and intelligent behaviour than dogs are: as a colony ants are able to farm and herd and they perform accounting of the number of ants trespassing on their territory.
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